Zmena v rekonstruction loss¶
Sparse Autoencodedry se nemuseji trenovat pouze na klasicke L2 loss, ale muzeme zvolit jine. Co se ukazalo, jako docela funkcni pro doporucovaci systemy, bylo pouzit cosine similarity jako loss. Podle papery to davalo opravdu dobre vysledky.
Table of reconstrictions metrics¶
comparision of the L2 loss (compare) and cosine similarity (main) reconstruction loss on the ELSA dataset.
- CS - Cosine Similarity of original and reconstructed embeddings
- Deads - Percentage of dead neurons in the sparse embedding
- Deg - Degradation of NDCG between ELSA model and ELSA + Autoencoder
|
Dimensions |
Expansion Ratio |
TopK |
LastFM1k |
MovieLens |
|
|
|
|
% change |
compare |
main |
% change |
compare |
main |
% change |
... |
main |
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
|
|
|
|
CS |
CS |
CS |
Deads |
Deads |
Deads |
Deg |
... |
Deg |
CS |
CS |
CS |
Deads |
Deads |
Deads |
Deg |
Deg |
Deg |
| 0 |
1024 |
4.0 |
32 |
0.0135 |
0.9026 |
0.9027 |
-10.4348 |
0.2246 |
0.2012 |
-37.7869 |
... |
-0.0184 |
-0.1005 |
0.9472 |
0.9462 |
NaN |
0.0000 |
0.0 |
-0.3955 |
-0.0119 |
-0.0120 |
| 1 |
1024 |
4.0 |
64 |
-0.3697 |
0.9256 |
0.9221 |
-20.0000 |
0.0830 |
0.0664 |
-176.6462 |
... |
-0.0182 |
-0.4022 |
0.9698 |
0.9659 |
NaN |
0.0000 |
0.0 |
4.4958 |
-0.0057 |
-0.0054 |
| 2 |
1024 |
4.0 |
128 |
-1.5272 |
0.9489 |
0.9344 |
-53.8462 |
0.0127 |
0.0059 |
-162.6340 |
... |
-0.0196 |
-1.1890 |
0.9914 |
0.9796 |
NaN |
0.0000 |
0.0 |
-71.8368 |
-0.0023 |
-0.0039 |
| 3 |
2048 |
8.0 |
32 |
0.8817 |
0.9024 |
0.9104 |
-31.7431 |
0.5322 |
0.3633 |
-802.4991 |
... |
-0.0183 |
-0.2358 |
0.9427 |
0.9405 |
NaN |
0.0000 |
0.0 |
-5.5714 |
-0.0144 |
-0.0152 |
| 4 |
2048 |
8.0 |
64 |
0.7415 |
0.9246 |
0.9315 |
-22.7626 |
0.2510 |
0.1938 |
-11.2530 |
... |
-0.0168 |
-0.6032 |
0.9658 |
0.9600 |
NaN |
0.0000 |
0.0 |
-17.2345 |
-0.0070 |
-0.0082 |
| 5 |
2048 |
8.0 |
128 |
-0.2503 |
0.9504 |
0.9481 |
-19.1919 |
0.0967 |
0.0781 |
43.3454 |
... |
-0.0106 |
-1.1276 |
0.9867 |
0.9756 |
NaN |
0.0000 |
0.0 |
-91.6178 |
-0.0025 |
-0.0047 |
| 6 |
4096 |
16.0 |
32 |
1.5373 |
0.8978 |
0.9116 |
-26.1170 |
0.7432 |
0.5491 |
-688.0801 |
... |
-0.0180 |
-0.4869 |
0.9410 |
0.9364 |
-100.0 |
0.0068 |
0.0 |
-13.3860 |
-0.0153 |
-0.0174 |
| 7 |
4096 |
16.0 |
64 |
1.4121 |
0.9237 |
0.9367 |
-32.8203 |
0.5393 |
0.3623 |
-5849.2522 |
... |
-0.0133 |
-0.6854 |
0.9605 |
0.9539 |
NaN |
0.0000 |
0.0 |
-12.9190 |
-0.0093 |
-0.0105 |
| 8 |
4096 |
16.0 |
128 |
0.2552 |
0.9496 |
0.9520 |
-24.6575 |
0.3030 |
0.2283 |
-117.7475 |
... |
-0.0184 |
-0.9140 |
0.9780 |
0.9691 |
NaN |
0.0000 |
0.0 |
-51.6352 |
-0.0045 |
-0.0068 |
9 rows × 21 columns
Means of above table¶
Dimensions 2389.333333
Expansion Ratio 9.333333
TopK 74.666667
LastFM1k % change CS 0.299344
compare CS 0.925067
main CS 0.927722
% change Deads -26.841489
compare Deads 0.309522
main Deads 0.227600
% change Deg -866.950400
compare Deg -0.008211
main Deg -0.016844
MovieLens % change CS -0.638289
compare CS 0.964789
main CS 0.958578
% change Deads -100.000000
compare Deads 0.000756
main Deads 0.000000
% change Deg -28.900044
compare Deg -0.008100
main Deg -0.009344
dtype: float64
Comparing the L2 variant (compare) with the cosine similarity variant (main)
|
Dataset |
Dimensions |
TopK |
G/mean |
Pop |
U/mean |
U/min |
|
|
|
|
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
| 0 |
LastFM1k |
1024 |
32 |
8.11 |
0.59 |
0.64 |
-1.51 |
0.62 |
0.61 |
0.22 |
0.79 |
0.80 |
-2.09 |
0.63 |
0.62 |
| 1 |
LastFM1k |
1024 |
64 |
1.90 |
0.58 |
0.59 |
0.07 |
0.61 |
0.61 |
-1.19 |
0.80 |
0.79 |
-4.65 |
0.63 |
0.60 |
| 2 |
LastFM1k |
1024 |
128 |
-11.80 |
0.60 |
0.53 |
0.08 |
0.60 |
0.60 |
-1.59 |
0.80 |
0.79 |
-1.39 |
0.63 |
0.62 |
| 3 |
LastFM1k |
2048 |
32 |
-7.01 |
0.59 |
0.55 |
3.35 |
0.64 |
0.67 |
0.03 |
0.79 |
0.79 |
-0.46 |
0.62 |
0.61 |
| 4 |
LastFM1k |
2048 |
64 |
-0.74 |
0.60 |
0.59 |
2.35 |
0.62 |
0.63 |
-2.00 |
0.81 |
0.79 |
-4.10 |
0.64 |
0.61 |
| 5 |
LastFM1k |
2048 |
128 |
10.38 |
0.61 |
0.67 |
0.55 |
0.61 |
0.62 |
-1.05 |
0.81 |
0.80 |
0.56 |
0.61 |
0.62 |
| 6 |
LastFM1k |
4096 |
32 |
12.87 |
0.57 |
0.65 |
-3.22 |
0.66 |
0.63 |
2.12 |
0.78 |
0.80 |
-0.11 |
0.63 |
0.62 |
| 7 |
LastFM1k |
4096 |
64 |
31.31 |
0.52 |
0.69 |
7.10 |
0.63 |
0.67 |
-2.10 |
0.81 |
0.79 |
-1.93 |
0.62 |
0.61 |
| 8 |
LastFM1k |
4096 |
128 |
-2.79 |
0.59 |
0.58 |
4.59 |
0.62 |
0.64 |
-2.50 |
0.81 |
0.79 |
-1.29 |
0.63 |
0.62 |
| 9 |
MovieLens |
1024 |
32 |
-14.22 |
0.58 |
0.50 |
-5.89 |
0.52 |
0.49 |
0.09 |
0.64 |
0.64 |
-2.94 |
0.52 |
0.50 |
| 10 |
MovieLens |
1024 |
64 |
22.13 |
0.54 |
0.66 |
-8.08 |
0.50 |
0.46 |
0.53 |
0.65 |
0.66 |
0.43 |
0.53 |
0.53 |
| 11 |
MovieLens |
1024 |
128 |
-0.40 |
0.65 |
0.65 |
1.98 |
0.49 |
0.50 |
-0.31 |
0.67 |
0.67 |
9.85 |
0.51 |
0.56 |
| 12 |
MovieLens |
2048 |
32 |
-47.37 |
0.68 |
0.36 |
-8.55 |
0.49 |
0.45 |
-6.13 |
0.66 |
0.61 |
-16.22 |
0.54 |
0.45 |
| 13 |
MovieLens |
2048 |
64 |
8.41 |
0.45 |
0.49 |
-2.29 |
0.48 |
0.47 |
-2.58 |
0.65 |
0.63 |
-8.22 |
0.53 |
0.49 |
| 14 |
MovieLens |
2048 |
128 |
15.85 |
0.51 |
0.59 |
-2.03 |
0.48 |
0.47 |
-2.50 |
0.67 |
0.65 |
2.63 |
0.53 |
0.54 |
| 15 |
MovieLens |
4096 |
32 |
-16.46 |
0.66 |
0.55 |
-0.78 |
0.48 |
0.48 |
-1.14 |
0.66 |
0.65 |
-8.17 |
0.55 |
0.50 |
| 16 |
MovieLens |
4096 |
64 |
0.75 |
0.59 |
0.59 |
-6.33 |
0.51 |
0.48 |
-2.49 |
0.66 |
0.64 |
-11.85 |
0.53 |
0.47 |
| 17 |
MovieLens |
4096 |
128 |
4.71 |
0.56 |
0.59 |
-1.73 |
0.49 |
0.48 |
-0.20 |
0.65 |
0.65 |
0.69 |
0.51 |
0.52 |
|
Dimensions |
TopK |
G/mean |
Pop |
U/mean |
U/min |
|
|
|
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
| Dataset |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| LastFM1k |
2389.333333 |
74.666667 |
4.692222 |
0.583333 |
0.610000 |
1.484444 |
0.623333 |
0.631111 |
-0.895556 |
0.800000 |
0.793333 |
-1.717778 |
0.626667 |
0.614444 |
| MovieLens |
2389.333333 |
74.666667 |
-2.955556 |
0.580000 |
0.553333 |
-3.744444 |
0.493333 |
0.475556 |
-1.636667 |
0.656667 |
0.644444 |
-3.755556 |
0.527778 |
0.506667 |
|
Dimensions |
TopK |
G/mean |
Pop |
U/mean |
U/min |
|
|
|
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
| Dataset |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| LastFM1k |
1354.624671 |
42.332021 |
12.853204 |
0.026458 |
0.055000 |
3.188911 |
0.018028 |
0.025221 |
1.459119 |
0.01118 |
0.005000 |
1.735733 |
0.008660 |
0.007265 |
| MovieLens |
1354.624671 |
42.332021 |
20.835766 |
0.075166 |
0.092871 |
3.602930 |
0.014142 |
0.015092 |
2.070628 |
0.01000 |
0.017401 |
8.094245 |
0.013017 |
0.034641 |
Comparing the L2 variant (compare) with the cosine similarity variant (main)
|
Dimensions |
TopK |
G/mean |
Pop |
U/mean |
U/min |
|
|
|
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
| Dataset |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| LastFM1k |
2389.333333 |
74.666667 |
-7.473333 |
0.438889 |
0.401111 |
1.584444 |
0.663333 |
0.674444 |
-1.593333 |
0.740000 |
0.728889 |
-3.428889 |
0.535556 |
0.516667 |
| MovieLens |
2389.333333 |
74.666667 |
-13.103333 |
0.605556 |
0.526667 |
-2.054444 |
0.504444 |
0.495556 |
-1.542222 |
0.621111 |
0.610000 |
-5.000000 |
0.478889 |
0.451111 |
Comparing the L2 variant (compare) with the cosine similarity variant (main)
|
Dataset |
Dimensions |
TopK |
G/mean |
Pop |
U/mean |
U/min |
|
|
|
|
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
| 0 |
LastFM1k |
1024 |
32 |
-1.94 |
0.44 |
0.43 |
-0.30 |
0.60 |
0.60 |
-4.19 |
0.65 |
0.62 |
-12.49 |
0.40 |
0.35 |
| 1 |
LastFM1k |
1024 |
64 |
30.11 |
0.38 |
0.49 |
-0.16 |
0.54 |
0.54 |
-4.49 |
0.61 |
0.58 |
-7.12 |
0.32 |
0.30 |
| 2 |
LastFM1k |
1024 |
128 |
15.82 |
0.29 |
0.34 |
-0.32 |
0.55 |
0.55 |
-3.68 |
0.60 |
0.58 |
-16.15 |
0.34 |
0.28 |
| 3 |
LastFM1k |
2048 |
32 |
12.41 |
0.50 |
0.56 |
6.99 |
0.66 |
0.70 |
-0.15 |
0.68 |
0.68 |
-7.70 |
0.43 |
0.40 |
| 4 |
LastFM1k |
2048 |
64 |
49.36 |
0.34 |
0.51 |
3.04 |
0.61 |
0.63 |
-4.01 |
0.65 |
0.62 |
-14.69 |
0.41 |
0.35 |
| 5 |
LastFM1k |
2048 |
128 |
70.61 |
0.30 |
0.51 |
9.05 |
0.58 |
0.63 |
-1.88 |
0.63 |
0.61 |
-0.51 |
0.34 |
0.34 |
| 6 |
LastFM1k |
4096 |
32 |
-19.33 |
0.56 |
0.45 |
0.96 |
0.67 |
0.68 |
-0.03 |
0.68 |
0.68 |
-8.08 |
0.45 |
0.42 |
| 7 |
LastFM1k |
4096 |
64 |
-2.15 |
0.53 |
0.51 |
9.94 |
0.64 |
0.70 |
1.15 |
0.67 |
0.67 |
-9.57 |
0.43 |
0.39 |
| 8 |
LastFM1k |
4096 |
128 |
-28.00 |
0.46 |
0.33 |
6.78 |
0.60 |
0.65 |
1.18 |
0.65 |
0.65 |
1.86 |
0.39 |
0.40 |
| 9 |
MovieLens |
1024 |
32 |
inf |
0.00 |
0.31 |
49.63 |
0.18 |
0.28 |
15.94 |
0.35 |
0.41 |
87.68 |
0.12 |
0.22 |
| 10 |
MovieLens |
1024 |
64 |
-32.11 |
0.12 |
0.08 |
-17.08 |
0.28 |
0.23 |
-10.37 |
0.48 |
0.43 |
-26.08 |
0.22 |
0.16 |
| 11 |
MovieLens |
1024 |
128 |
-68.80 |
0.38 |
0.12 |
24.24 |
0.26 |
0.32 |
16.33 |
0.46 |
0.53 |
10.49 |
0.25 |
0.28 |
| 12 |
MovieLens |
2048 |
32 |
NaN |
0.00 |
0.00 |
22.52 |
0.21 |
0.26 |
-23.62 |
0.43 |
0.33 |
-42.61 |
0.21 |
0.12 |
| 13 |
MovieLens |
2048 |
64 |
-62.84 |
0.20 |
0.07 |
-11.92 |
0.22 |
0.20 |
-11.43 |
0.40 |
0.35 |
-15.07 |
0.12 |
0.10 |
| 14 |
MovieLens |
2048 |
128 |
-7.49 |
0.08 |
0.08 |
-12.15 |
0.31 |
0.27 |
-1.28 |
0.48 |
0.48 |
-0.76 |
0.26 |
0.26 |
| 15 |
MovieLens |
4096 |
32 |
inf |
0.00 |
0.09 |
36.13 |
0.29 |
0.40 |
2.00 |
0.51 |
0.52 |
13.27 |
0.31 |
0.35 |
| 16 |
MovieLens |
4096 |
64 |
inf |
0.00 |
0.23 |
25.94 |
0.25 |
0.31 |
-4.56 |
0.42 |
0.40 |
-10.76 |
0.23 |
0.20 |
| 17 |
MovieLens |
4096 |
128 |
-74.65 |
0.38 |
0.10 |
-6.40 |
0.35 |
0.33 |
-5.42 |
0.48 |
0.46 |
7.88 |
0.24 |
0.26 |
|
Dimensions |
TopK |
G/mean |
Pop |
U/mean |
U/min |
|
|
|
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
| Dataset |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| LastFM1k |
2389.333333 |
74.666667 |
14.098889 |
0.422222 |
0.458889 |
3.997778 |
0.605556 |
0.631111 |
-1.788889 |
0.646667 |
0.632222 |
-8.272222 |
0.390000 |
0.358889 |
| MovieLens |
2389.333333 |
74.666667 |
inf |
0.128889 |
0.120000 |
12.323333 |
0.261111 |
0.288889 |
-2.490000 |
0.445556 |
0.434444 |
2.671111 |
0.217778 |
0.216667 |
Comparing the L2 variant (compare) with the cosine similarity variant (main)
|
Dataset |
Dimensions |
TopK |
G/mean |
Pop |
U/mean |
U/min |
|
|
|
|
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
| 0 |
LastFM1k |
1024 |
32 |
18.74 |
0.52 |
0.62 |
-2.24 |
0.60 |
0.59 |
-0.59 |
0.81 |
0.80 |
3.43 |
0.64 |
0.66 |
| 1 |
LastFM1k |
1024 |
64 |
0.54 |
0.56 |
0.56 |
-3.51 |
0.61 |
0.59 |
-0.54 |
0.81 |
0.81 |
-1.74 |
0.65 |
0.64 |
| 2 |
LastFM1k |
1024 |
128 |
0.25 |
0.57 |
0.57 |
-3.20 |
0.61 |
0.59 |
-0.38 |
0.81 |
0.81 |
-3.58 |
0.65 |
0.63 |
| 3 |
LastFM1k |
2048 |
32 |
21.15 |
0.58 |
0.71 |
-2.64 |
0.62 |
0.60 |
1.88 |
0.82 |
0.83 |
6.20 |
0.64 |
0.68 |
| 4 |
LastFM1k |
2048 |
64 |
23.06 |
0.58 |
0.71 |
-1.64 |
0.61 |
0.60 |
-0.12 |
0.82 |
0.82 |
2.41 |
0.67 |
0.68 |
| 5 |
LastFM1k |
2048 |
128 |
7.23 |
0.65 |
0.69 |
1.56 |
0.60 |
0.61 |
0.57 |
0.82 |
0.82 |
-0.05 |
0.67 |
0.67 |
| 6 |
LastFM1k |
4096 |
32 |
14.17 |
0.59 |
0.67 |
-6.78 |
0.61 |
0.57 |
1.33 |
0.81 |
0.82 |
6.25 |
0.65 |
0.69 |
| 7 |
LastFM1k |
4096 |
64 |
21.96 |
0.58 |
0.71 |
-1.29 |
0.61 |
0.60 |
1.07 |
0.82 |
0.83 |
5.70 |
0.65 |
0.69 |
| 8 |
LastFM1k |
4096 |
128 |
-2.55 |
0.62 |
0.60 |
-1.84 |
0.61 |
0.60 |
0.72 |
0.82 |
0.82 |
2.68 |
0.64 |
0.66 |
| 9 |
MovieLens |
1024 |
32 |
13.53 |
0.59 |
0.67 |
-6.49 |
0.53 |
0.50 |
0.33 |
0.69 |
0.69 |
-2.09 |
0.58 |
0.57 |
| 10 |
MovieLens |
1024 |
64 |
-9.81 |
0.74 |
0.67 |
-2.18 |
0.54 |
0.53 |
-0.55 |
0.70 |
0.69 |
0.56 |
0.58 |
0.58 |
| 11 |
MovieLens |
1024 |
128 |
3.07 |
0.66 |
0.68 |
0.52 |
0.53 |
0.54 |
-0.05 |
0.69 |
0.69 |
-0.21 |
0.58 |
0.57 |
| 12 |
MovieLens |
2048 |
32 |
-11.15 |
0.66 |
0.58 |
-7.44 |
0.54 |
0.50 |
-0.09 |
0.69 |
0.69 |
-2.34 |
0.58 |
0.57 |
| 13 |
MovieLens |
2048 |
64 |
-1.07 |
0.67 |
0.66 |
-1.43 |
0.53 |
0.53 |
-0.52 |
0.69 |
0.69 |
-1.48 |
0.58 |
0.57 |
| 14 |
MovieLens |
2048 |
128 |
-7.85 |
0.70 |
0.65 |
1.94 |
0.53 |
0.54 |
-0.70 |
0.69 |
0.69 |
-0.25 |
0.57 |
0.57 |
| 15 |
MovieLens |
4096 |
32 |
12.77 |
0.57 |
0.65 |
-6.46 |
0.54 |
0.51 |
0.07 |
0.68 |
0.68 |
1.37 |
0.56 |
0.57 |
| 16 |
MovieLens |
4096 |
64 |
-26.16 |
0.69 |
0.51 |
-4.42 |
0.54 |
0.52 |
0.41 |
0.69 |
0.69 |
-2.53 |
0.59 |
0.57 |
| 17 |
MovieLens |
4096 |
128 |
-18.62 |
0.68 |
0.56 |
-0.84 |
0.53 |
0.53 |
0.00 |
0.69 |
0.69 |
-3.06 |
0.58 |
0.57 |
Comparing the L2 variant (compare) with the cosine similarity variant (main)
|
Dataset |
Dimensions |
TopK |
G/mean |
Pop |
U/mean |
U/min |
|
|
|
|
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
| 0 |
LastFM1k |
1024 |
32 |
6.58 |
0.40 |
0.42 |
-4.49 |
0.66 |
0.63 |
0.25 |
0.75 |
0.75 |
1.28 |
0.56 |
0.56 |
| 1 |
LastFM1k |
1024 |
64 |
-13.11 |
0.43 |
0.37 |
-3.33 |
0.66 |
0.64 |
-1.49 |
0.75 |
0.74 |
-4.14 |
0.55 |
0.53 |
| 2 |
LastFM1k |
1024 |
128 |
-13.67 |
0.36 |
0.31 |
-5.05 |
0.66 |
0.62 |
-2.97 |
0.75 |
0.73 |
-1.62 |
0.56 |
0.55 |
| 3 |
LastFM1k |
2048 |
32 |
-12.22 |
0.50 |
0.44 |
-0.71 |
0.66 |
0.66 |
1.50 |
0.76 |
0.78 |
4.66 |
0.59 |
0.62 |
| 4 |
LastFM1k |
2048 |
64 |
6.74 |
0.42 |
0.45 |
-0.98 |
0.66 |
0.66 |
2.01 |
0.76 |
0.77 |
1.99 |
0.58 |
0.59 |
| 5 |
LastFM1k |
2048 |
128 |
-20.85 |
0.50 |
0.40 |
-1.13 |
0.66 |
0.65 |
-0.22 |
0.77 |
0.76 |
-0.13 |
0.58 |
0.58 |
| 6 |
LastFM1k |
4096 |
32 |
4.33 |
0.36 |
0.38 |
-6.09 |
0.67 |
0.63 |
1.67 |
0.76 |
0.78 |
5.94 |
0.57 |
0.60 |
| 7 |
LastFM1k |
4096 |
64 |
-0.74 |
0.36 |
0.36 |
-0.72 |
0.66 |
0.65 |
0.94 |
0.75 |
0.76 |
1.14 |
0.58 |
0.59 |
| 8 |
LastFM1k |
4096 |
128 |
5.57 |
0.35 |
0.37 |
-0.98 |
0.66 |
0.65 |
1.40 |
0.76 |
0.77 |
1.88 |
0.56 |
0.57 |
| 9 |
MovieLens |
1024 |
32 |
-2.26 |
0.59 |
0.57 |
-7.80 |
0.57 |
0.53 |
-2.35 |
0.69 |
0.67 |
-7.39 |
0.56 |
0.51 |
| 10 |
MovieLens |
1024 |
64 |
-1.19 |
0.61 |
0.60 |
-1.41 |
0.57 |
0.56 |
-0.66 |
0.69 |
0.69 |
-0.98 |
0.55 |
0.55 |
| 11 |
MovieLens |
1024 |
128 |
13.88 |
0.54 |
0.62 |
0.30 |
0.57 |
0.57 |
0.29 |
0.69 |
0.69 |
0.88 |
0.54 |
0.55 |
| 12 |
MovieLens |
2048 |
32 |
-6.81 |
0.63 |
0.58 |
-6.32 |
0.57 |
0.54 |
-2.54 |
0.69 |
0.67 |
-5.89 |
0.55 |
0.51 |
| 13 |
MovieLens |
2048 |
64 |
23.29 |
0.55 |
0.68 |
-0.82 |
0.58 |
0.57 |
-0.16 |
0.69 |
0.69 |
1.05 |
0.55 |
0.55 |
| 14 |
MovieLens |
2048 |
128 |
-0.35 |
0.62 |
0.62 |
0.87 |
0.57 |
0.58 |
0.07 |
0.69 |
0.69 |
-0.66 |
0.56 |
0.55 |
| 15 |
MovieLens |
4096 |
32 |
-9.77 |
0.57 |
0.51 |
-6.08 |
0.58 |
0.54 |
-2.97 |
0.69 |
0.67 |
-1.84 |
0.54 |
0.53 |
| 16 |
MovieLens |
4096 |
64 |
24.47 |
0.54 |
0.67 |
-4.39 |
0.57 |
0.55 |
-2.62 |
0.69 |
0.67 |
1.01 |
0.53 |
0.54 |
| 17 |
MovieLens |
4096 |
128 |
-0.25 |
0.62 |
0.61 |
1.56 |
0.56 |
0.57 |
-0.74 |
0.69 |
0.68 |
1.38 |
0.54 |
0.54 |
Comparing the L2 variant (compare) with the cosine similarity variant (main)
|
Dataset |
Dimensions |
TopK |
G/mean |
Pop |
U/mean |
U/min |
|
|
|
|
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
% change |
compare |
main |
| 0 |
LastFM1k |
1024 |
32 |
-7.44 |
0.50 |
0.47 |
-13.21 |
0.63 |
0.55 |
-6.09 |
0.67 |
0.63 |
-6.14 |
0.46 |
0.43 |
| 1 |
LastFM1k |
1024 |
64 |
-38.73 |
0.46 |
0.28 |
-11.76 |
0.61 |
0.54 |
-6.01 |
0.66 |
0.62 |
-19.40 |
0.44 |
0.36 |
| 2 |
LastFM1k |
1024 |
128 |
-11.47 |
0.41 |
0.37 |
-16.07 |
0.60 |
0.50 |
-9.63 |
0.66 |
0.60 |
-19.77 |
0.42 |
0.34 |
| 3 |
LastFM1k |
2048 |
32 |
20.99 |
0.43 |
0.53 |
-4.23 |
0.62 |
0.59 |
-0.27 |
0.68 |
0.68 |
2.91 |
0.48 |
0.50 |
| 4 |
LastFM1k |
2048 |
64 |
-8.27 |
0.45 |
0.41 |
-3.94 |
0.61 |
0.59 |
-1.40 |
0.67 |
0.66 |
2.43 |
0.46 |
0.47 |
| 5 |
LastFM1k |
2048 |
128 |
2.81 |
0.47 |
0.48 |
-3.50 |
0.61 |
0.59 |
-1.68 |
0.66 |
0.65 |
4.68 |
0.44 |
0.46 |
| 6 |
LastFM1k |
4096 |
32 |
-26.41 |
0.52 |
0.38 |
-11.21 |
0.62 |
0.55 |
-0.77 |
0.68 |
0.67 |
-1.04 |
0.47 |
0.46 |
| 7 |
LastFM1k |
4096 |
64 |
12.58 |
0.47 |
0.52 |
-0.93 |
0.61 |
0.60 |
-0.35 |
0.68 |
0.68 |
-0.41 |
0.46 |
0.46 |
| 8 |
LastFM1k |
4096 |
128 |
4.67 |
0.45 |
0.47 |
-4.21 |
0.61 |
0.58 |
-1.28 |
0.66 |
0.65 |
-1.04 |
0.45 |
0.44 |
| 9 |
MovieLens |
1024 |
32 |
-36.91 |
0.15 |
0.10 |
-35.73 |
0.43 |
0.27 |
-16.38 |
0.62 |
0.52 |
-27.83 |
0.45 |
0.32 |
| 10 |
MovieLens |
1024 |
64 |
0.00 |
0.13 |
0.13 |
-9.56 |
0.42 |
0.38 |
-4.12 |
0.62 |
0.60 |
-8.25 |
0.46 |
0.43 |
| 11 |
MovieLens |
1024 |
128 |
-7.92 |
0.12 |
0.11 |
-10.21 |
0.42 |
0.38 |
-4.52 |
0.63 |
0.60 |
-4.21 |
0.44 |
0.42 |
| 12 |
MovieLens |
2048 |
32 |
-42.19 |
0.15 |
0.09 |
-45.71 |
0.44 |
0.24 |
-21.89 |
0.63 |
0.49 |
-35.32 |
0.43 |
0.28 |
| 13 |
MovieLens |
2048 |
64 |
0.00 |
0.12 |
0.12 |
-22.09 |
0.43 |
0.34 |
-10.39 |
0.62 |
0.56 |
-14.93 |
0.44 |
0.37 |
| 14 |
MovieLens |
2048 |
128 |
16.10 |
0.13 |
0.15 |
-2.36 |
0.40 |
0.39 |
-0.54 |
0.61 |
0.60 |
-1.50 |
0.42 |
0.41 |
| 15 |
MovieLens |
4096 |
32 |
40.37 |
0.11 |
0.15 |
-47.08 |
0.45 |
0.24 |
-22.97 |
0.64 |
0.49 |
-41.66 |
0.47 |
0.28 |
| 16 |
MovieLens |
4096 |
64 |
-28.06 |
0.10 |
0.07 |
-36.17 |
0.45 |
0.28 |
-17.50 |
0.63 |
0.52 |
-32.75 |
0.46 |
0.31 |
| 17 |
MovieLens |
4096 |
128 |
16.10 |
0.13 |
0.15 |
-23.98 |
0.40 |
0.30 |
-12.23 |
0.62 |
0.55 |
-24.51 |
0.42 |
0.32 |